Fermion Hamiltonians with Monopole and Quadrupole Pairing

Abstract

In this workshop we have seen evidence that the interacting boson model (IBM) seems to provide a unified phenomenological model of vibrational, transitional, and rotational nuclei. The underlying concept of this model is that the low-lying collective states of heavy nuclei are made up of monopole and quadrupole Bosons &† and d _μ† bosons where µ = -2, -1, 0, 1, 2. These bosons can be interpreted to represent correlated pairs of valence nucleons outside the closed core. Hence a natural view of the IBM is that it is an approximation to the complicated shell model description of these heavy nuclei. That is, the valence nucleons move in an average field and the residual. interactions produce correlated monopole, St, and quadrupole, D_μ†, pairs of valence nucleons. The collective low-lying states are then comprised mostly of these pairs, and the effect of the many other more complicated states is mainly to renormalize the shell model Hamiltonian and transition operators.